Relay desing calculator



Dfli. 2, 1947. w, KEISTER 2,431,696

RELAY DESIGN CALCULATOR Filed Aug. 25, 1944 s Sheets-Sheet 1 I I I I;

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RELAY DESIGN CALCULATOR Filed Aug. 23, 1944 3 Sheets-Sheet 3 PROTECTIVE0N Res/sun t 44] 7- MAX. 0.

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i INVENTOR M. KE/STER 1 B @a M A TTORNE Y Patented Dec. 2, 1 947 RELAYDESIGN CALCULATOR William Keis ter, Short Hills, N. J., assignor to BellTelephone Laboratories, Incorporated, New York, N. Y., a corporation ofNew York Application August 23, 1944, Serial No. 550,843

11 Claims. (Cl. 235-61) mination necessitates considerable calculationbecause the data and formulae cannot be of a positive nature and theproper winding must be obtained by balancing the various factorsinvolved.

Similarly the operating time of the relay can be calculated directlywhen the design of the relay and the circuit conditions are known, butwhen a relay is to be designed to operate in a given time, large numbersof calculations may be required before a design is arrived at which willsatisfy all of the requirements.

In accordance with the present invention, means is provided for makingthe mathematical calculations necessary for relay winding design byelectrical means. More specifically, a multiple Wheatstone bridge isprovided whereby the bridge when balanced in connection with givenquantities will indicate the corresponding values of the remainingvariables required for the design of that relay winding. .In themultiple Wheatstone bridge formingthe subject-matter of this inventionat least two of the legs are varied simultaneously in a plurality of theindividual bridges. According to oneform of the invention, the circuitsare so arranged that the same galvanometer may serve a plurality ofindividual bridges.

These and other features of the invention will be more clearlyunderstood from a consideration of the following description read inconnection wifh the drawings in which:

Fig. 1 shows the basic relationship between the physical quantitiesemployed in designing relay windings;

Fig. 2 shows the practical circuits employed in suchabridge; while,

Fig. 3. shows a typical panel board for such a bridge;

Fig. 4 shows a theoretical multiple bridge for determining the time ofoperation of relays; and

Fig. 5 shows a practical circuit employed in a bridge of the type ofFig. 4.

structurally, the design of a relay winding involves the size of thespace in which the winding is to be located and the size of the wire.These functions in turn involve the diameter of the core, the length ofthe core on which the; wire is to be wound and the depth of the Windingas well as the gauge and insulation of the wire itself, which determinesthe number of turns and number of layers which may be placed in thespace available. Electrically, the voltage and current being used andthe resistivity of the wire must be considered; I

The principal formulae used in the calculations necessary for relaywinding design are as follows:

where L=length of coil in inches B=effective breadth of one wire.

The number of layers which may be wound in a given space may beexpressed by the equation i where h=depth of coil space C=efiectivedepth of one wire filler.

The number of turns which may be used may be expressed by the equation Iincluding insulating Calculations relating to resistance To obtainresistance when the number of turns, gauge of wire and dimensions ofwinding space are given:

From the formulas set-forth at page 504 of the Standard Handbook forElectrical Engineers, seventh edition, the total resistance of a relayWinding may be stated where =ohms per unit length of the wire, andf=length of a mean turn in inches.

where d: diameter of the core.

From Equation 3 the value of h may be derived as where K=B C=efiective Vcross section 'of one turn of wire.

Hence Equation 3a may be written A bulge factor do is sometimes used toallow for-the 'fact that the first layer of 'the'coil may :not fitsnugly against-the.core and has the effect or increasing the apparentcore'diameter. Therefore,

Total resistance R is in accordancecwith the equation where theresistivity factor A which may be determined from one of the followingequations:

When the resistance, number of turns and coil dimensions'are-given I R*N(h+d+ d. When the desired-voltage, ampereturn-s and "coil dimensionsare given ..E Nl (h+d+a (6) where E=voltage I=current in amperes.

When the resistance and coil dimensions are given The general theory onwhich'is based the use of the Wheatstone bridge for solving mathematicalequations maybe set forth as follows:

The balance condition for an zordinaliy Whe tstone bridge-is representedby theequations ,4 where R1, R2, R3 and R4 are the values of theresistances in the four arms of the bridge. If a mathematical equationcan be put in the form of either Equations 8a or 812 it can be solved bymeans of a bridge. It is only necessary to choose scale factors andcalibrate the various resistances to represent corresponding variables.Then any setting of the resistances which balances the bridge givesconcurrent-values of the variables.

The *scalefactor isa constant which relates ohms resistance in thebridge to units of the corresponding variable in the mathematical equa---tion. Forexample, if the resistance R1 represents a variable'X and itis determined that 10 ohms lshallrepresentmneunit of X we have whereRl-iS in ohms.

This may be expressed R1= X (9b) Here ,u is the scale factor of X and inthis example ,u=10.

Scaleiac'torsareot two'types, Inkonecase the scale factor is anarbitraryconstantchosen to give. reasonable values of resistance-or to--obtain satisfactory balance over a given range of variables. In theothercase it is-necessaryto hold one or more members of the bridge ata-fixed value in order'to make the bridge Equation 8 conform to a givenmathematical formula. This scalefactor depends on the value chosen-forthe fixed resistance.

For scale factorsof the first type consider a mathematical equation ofthe iorm It is obvious'tha't' the validity' o'j this equation is notaffected by the introduction of arbitrary constants n1, #2, #3 and #4 inany of the following ways,

or, in genera mm X "mm Z ='R3=n2,c':i .R4.=7 ,142#4Z *I-Iere, ,ul g'isthe scale'factor or W," 1 i4 the scale factor ofX, etc., and Ri R4 areinunits of resistance (ohms).

The second "type of scale factor has a value depending onsomefixe'dresistance'in the bridge. For example,- considerimplemultiplication,

introducing la .con.st' mt, this may be elven the form of the bridgeequations (.8).

5 Type one scale factors may now be introduced in any of several ways asdiscussed above. For example:

HaX u K 1 Z MY m Referring to (8a), [.LSKI corresponds to R3 and bychoosing an appropriate fixed value Rx for this resistance the value ofK1 can be determined as follows:

where Rx is expressed in units of resistance. Now, substituting in (110)Comparing this with (812) In a particular example suppose that X hasvalues between 0.1 and 0.5 and Y has values between 20 and 100 and it isdesired to represent X and Y with resistances Varying from 1000 to 5000ohms.

If 1000 ohms is to represent a value of 0.1 for X, then Likewise 1 00H4=gF= 50 Choosing a resistance of 2500 ohms as appropriate for Rx, then(11c) gives,

(10,000X) (50 Y) (W (10.000X) (50 Y) (200Z) (2500) Comparing this with(8b) and taking the unit of resistance as one ohm.

R1=10,000X ohms R4=50Y ohms R2=200Z ohms Rs=2500 ohms The values for thebridge for solving (11), XY=Z then may be tabulated as follows:

Calibra- Scale Range of Range of Reslstame variable Factor 1 VariableResistance Ohms X 10, 000 001 0. 1-0. 5 1, 000-5, 000 Y 50 02 20-100 1,000-5, 000 Z 200 O05 2-50 40040, 000 2500 ohms Fixed Resistance Anequation which includes addition in conjunction with multiplication canbe solved by connecting two variable resistances in series" in one ormore arms of the bridge. a formula such as may be handled by introducinga constant, K1; asin (11),

For example,

Further scale factors may be introduced and both Y and Z will have thesame scale factors.

Quadratic equations such as may be solved by using two resistancescalibrated in terms of a: and coupled together to be controlled by thesame set of knobs. Equation 13 must first be put in the form of (8),thus Scale factors may now be introduced #11 3 l zl s i Now, choose anappropriate fixed resistance RK and set [LB/13K 1=RK, then,

=fit. 1 mm Hence,

mm K mi -mus #2H4( (13b) where c=d+dc=inside diameter of coil in inchesincluding bulge allowance.

From Equation 3 it is apparent that the depth, h, of the winding ininches is given by,

R=AN (14) So that (14) becomes,

R=AN(h+c) (16) This is of the form (8a) and may be solved by means of abridge.

The value of it can be determined by a second independent bridge becauseformula (15) can be expressed as If the two h and two N resistances of(15a) and (16a) are mechanically coupled, a dual bridge results as shownschematically in Fig. 1 and, since the resistance representing aredependent on wire size they may also be mechanically coupled.

A form wound coil is wound to even layers and in specifications of suchcoils it is usual to give the turns per layer 711, and the number oflayers, These calculations may be made by modifications of bridge 2 asfollows:

The equation of bridge 2 is,

Values of m and 122 may be obtained from the following equations:

h e (17) with resistance replacing K and in replacing with C replacingK, vii r'eplacing'N and L replaced by a fixed resistance which may bedesignated in.

Acircuit for the dual bridge of Fig. 1 is shown in Fig. 2 and thearrangement of the control dials is shown in Fig. 3, the same referencecharacters being used in Figs. 1 and 2. The resistances which representthe values of N, R, m, m, h, L and c are in the form of decaderesistances for convenience in reading the setting. The dials whichcontrol the resistances, representing N and h, vary two sets ofresistances simultaneously, while the resistances which represent 1 "A"uv: max and C are varied simultaneously by a single dial. Since theeffective size of the wire has a different range for different types ofinsulation, aswitch 21s is provided which may be set in any one of threepositions to render a difierent set of resistances available inaccordance with the insulation to be used; A switch 203 is used toinclude one of the resistances MA to IMF in a circuit depending on theinside diameter of the coil to be designed. While it would be possibleto use the variable resistance IMA for all calculations, certain coresizes recur so frequently as to make it' convenient to use fixedresistances for their values. Similarly, a number of fixed resistanceslEiiA2 to IU9A4 are used to correspond to the length of the most commontypes of relays with a variable resistance HJSAI for unusual types, theswitch 264 servin to include the desired resistance.

Key 289 when operated supplies battery to the circuits throughresistance 29!. Key 215 is used to include either the average or themaximum value of the resistance corresponding to K in the circuit. Whenkey 2l'5 is normal, the average value of K is employed while with key2l5 operated the maximumvalue of K is employed. Key 262- is a three-waykey. When in its normal position it serves to place bridge 2 incondition to solve the fundamental equation of the bridge,

that is, Equation 14. With key 202 moved to the left it arranges thecircuit to'solve the equation involving turns per layer (111) that isEquation 1'7 and with key 202 moved to the right the bridge is arrangedto solve Equation 18 which involves the number of layers (112); It iscustomary with certain types of relays to allow one-fifth layer forpossible variation and key ZES is used to make this allowance whenrequired; V

The solution of a winding'problem bythe use of the dual bridge of Fig. 2requires that both bridges be balanced. In most cases this is notdifiicult since several of the variables are known and these values canbe set and only the remaining dial need be manipulated to obtain abalance. For convenience in adjusting the bridges, tables 353i and 382located on the face of the panel show the adjustments which will tend tobring the bridge into balance when the deflections of the galvanometersare to the right or the left of zero.

A typical problem will indicate the manner in which the bridge may beused. Assume first that it is desired to know the resistance of the coilwhich will result from the use of a given number of turns of wire of agiven size in a coil of known dimensions. None of the keys 29G, 2|5 or265 is operated. Switches 203 and 204 are set on the proper dimensionsof coils, switch 219 is set on the type of wire, for example, in theposition shown, which corresponds to filled enamel wire, and the switch303 is positioned to the proper gauge thereby simultaneously adjustingresistances lElZA of the bridge I and resistances IliSAl, iiifiAZ andliifiA3 which belong to the bridge 2. Dials 326 to 323 are then operatedto positions indicating the desired'number of turns resulting in thesimultaneous adjustment of resistance ID!) of bridge I and resistanceI68 of bridge 2. Key 28! is then operated to supply battery to thebridges and the dials 35B, 35I and 352, corre sponding to depth of coil,are adjusted until bridge 2 is balanced, atwhich time Equation 15a willbe satisfied. Thereafter dials am to 3ft, corresponding to resistance,are adjusted until bridge I is balanced. The values of the resistancemay then be read from the corresponding dials. If, after the solutionhas been obtained as above, it is desired to find the number of layersnecessary to produce the desired winding, the dial and switches are leftin the positions obtained and key 2:32 is thrown to its right-handposition. In this position it will be apparent that resistance Hi7 issubstituted for resistance I88 and resistance I 98A3 for resistanceIOGAI, while the fixed resistance 39C (111) is substituted for thevariable resistance IEJSAI. Adjustment of the dials 34!), SM, 342,corresponding to (m), until-bridgeZ is balanced will indicate the numberof layers by the positions assumed by the dials. On the other hand if itis desired to know the number of turns per layer, key 262 is thrown tothe left substituting resistance 393 (m) for one of the resistances1519A (L) and resistance IQS AS (C) for resistance IBGA! (Kav).Adjustment of dials 33$; 33!, and 332, corresponding to (721), untilbridge 2 is balanced will give an indication of the number of turns perlayer under the conditions set up.

A form of the multiple Wheatstone bridge which may be used indetermining the time of operation of relays is shown in Figs. 4 and 5. Alarge mum-- ber of variables must be considered in determining theoperating time of a relay. The determination of the operating time isfairly simple When the relay design and .circuit conditions are knownbut the designo'ff a relay to operate in a given time is diflicultbecause of this large number of variables. For example, if only thespring load and the circuit voltage are known, a relay may be designedto meet a given operating time requirement by assuming a resistance anddetermining the corresponding number of turns but this may result in arelay which is impossible to obtain in a standard relay structure. Otherresistance values must then be tried until a practical relay is found orit is determined that it is impossible to meet a given time requirement.With the multiple bridge of Figs. 4 and 5 many of the individualcalculations are made simultaneously and automatically so that trialsmay be made quickly and the complete range of possible coils explored toobtain the most satisfactory ones in a reasonable length of time.

The fundamental equations employed in the determination of relayoperating time have been derived in the Journal of the Institute ofElectrical Engineers, volume 66, No. 376, April 1928, are as follows:

where t=operating time of the relay T=time constant of the relay coilT1=time constant of core structure including Equations 19, 20 and 21 maybe combined into I These equations may be restated as the followingbridge type equations i may be derived from T and N by means of Equation26; the value of the ratio of i/I may be determined from the quantitiesE, R and i by means of Equation 25; the ratio T/Ki may be derived from Nand R by means of Equation 24 and the value of T derived from that ratioby means of Equation 27. Equation 23 combines the results secured fromthe other four equations to obtain the operating time t. These fiveequations are applied to the five bridges A, B, C, D and E forming themultiple bridge of Fig. 4.

The arrangement shown in Fig. 4 requires five galvanometers 454, 424,434, 444 and 454. It would, of course, be possible to use a singlegalvanometer with a switch to connect it into any one of the bridges, inwhich case the bridges would be balanced one at at ime. A moresatisfactory arrangement is that shown in Fig. 5 which employs twogalvanometers 503 and 504 permitting two bridges to be balancedsimultaneously.

The use of galvanometers 503 and 504 is controlled by a three-positionswitch 502. When this switch is normal the galvanometers are associatedwith bridges A and C, galvanometer 503 being connected over contact I2of key 502 to the junction between resistances 4i 0 and 4! 2representing the quantities E and R and over contact l0 of key 502 tothe junction between resistances 4H and 4 l 3 representing thequantities '& zandtween resistances 42| and 423 representing thequantities uT and N, respectively, and over contacts l5 and 0 of key 502to the junction between resistances 420 and 422 representing thequantities i and Rh, respectively. When the right-hand springs of key502 are operated, galvanometers 503 and 504 are connected in bridges Dand E,'galvanometer 503 being connected over contact 9 of key 502 to thejunction between resistances 43| and 433 representing the quantitiesT+T1 and t and over contact I l of key 502 to the junction betweenresistances 430 and 432 representing the quantities R, and log,

galvanometer 504 being connected over contact [4 of key 502 to thejunction between resistances 441 and 443 representing the quantities andover contact [6 of key 502 to the junction between resistances 440 and442 representing the quantities T and K1, respectively.

As in the multiple bridge of Fig. 2, a switch 505 is provided forselecting the value of T1 corresponding to the size of core and a switch506 for selecting the value of K1 corresponding to the various types ofrelays. Where the quantity such as R, i, T, etc., appears in more thanone bridge, the two values are adjusted simultaneously by a and R l 1common control dial. However, it is to be noted that thefunctions of theresistances shown as resistances 423 and 452 in Fig. .4 are performed.by a single resistance in the circuit of Fig. and likewisethe functionsof the resistances shown as resistances MI and 450 in Fig. 4,areperformed by a single resistance of Fig. 5. Resistances Rb, Rd and Reare fixed resistances representing the value of the numeral l in bridgesB, D and E in Fi 4.

The general operating procedure would be as follows: In the usualproblem the values of N, R, E and i are known and the value of t isdesired. In addition the values of K1 and T1 are determined by the typeof relay under consideration. The resistances representing the knownquantities are set, after which key 500 is operated to supply battery tothe bridges. With key 502 normal the resistance 4l3 representing thequantity in bridge E, and resistance 450 representing the quantit log,

1 is adjusted to balance the bridge C by means of galvanometer 504,thereby fixing the value of this resistance for use in bridge D. Key 502is now thrown to the right and resistance 440 representing the quantityT is adjusted to balance bridge D by means of galvanometer 504 at thesame time setting resistance 43! in bridge E. Bridge E is then balanced,using galvanometer 583, by adjusting resistance 433 to arrive at thevalue of t which gives the operating time.

Where the operate adjustment of the relay under consideration is knownin terms of ocT rather than 2', the value of i is determined by means ofbridge B. The left-hand'contacts of key 502 are operated and the knownvalues of aT and N set by the adjustment of'resistances 42! and. 423.Bridge B is then balanced, using galvanometer .584, by adjustingresistance 420150 arrive at the value of z, and set its value in bridgeA, after which the calculations proceed 'asabove described.

When insufiicient variables are known, such as designing a relay to meetgiven time requirements, arbitrary values are assumed for the requiredvariables and the remaining values determined, trials being made until asatisfactory relation is attained or until it is found that therequirement cannot be met with standard r elay structures.

All of the variables with the exception of the quantities I %and log, 1.

are represented by. decade resistances such as indicated for themultiple bridge of Fig. 3-but these two arms will be special slide wireresistances. The

arm is a linear resistance having the slide directly coupled to thedialon the panel which is calibrated to correspond. The resistance usedfor the quantity is wound on a fiat strip, the contour of which ismathematically determined to conform to that quantity and the slide ofWhich is mechanically coupled with the slide on the resistancerepresenting the quantity ing resistances calibrated to representcertain of said variables, one of the variables represented in eachbridge being also represented in another one of said bridges, eachbridge indicating a known relationship between the included variableswhen balanced, means for simultaneously adjusting all resistancesrepresenting the same variable, means for adjusting the remainingresistances to balance said bridges, and means for individualizing saidgalvanometers to said bridges to indicate when balances are reached.

2. A compound Wheatstone bridge for making calculations involving morethan four variables, comprising five bridges, two galvanometers, each ofsaid bridges comprising resistances calibrated to represent certain ofsaid variables, one of the variables represented in each bridge beingalso represented in another one of said bridges, each bridge indicatinga known relationship between the included variables when balanced, meansfor simultaneously adjusting all resistances repr senting the samevariable, means for adjusting the remaining resistances to balance saidbridges and means for individualizing said galvanometers to said bridgesin pairs to indicate when balance are reached.

3. A compound Wheatstone bridge for making calculations involving morethan four variables comprising five bridges, each composed ofresistances calibrated to represent certain of said variables, at leasttwo of the variables represented by arms of each of said bridgesappearing as arms of another one of said bridges, each bridge indicatinga known relationship between the included variables when balanced, meansfor simultaneously adjusting all resistances representing the samevariables, means for adjusting the remaining resistances to balance saidbridges, two galvanometers, and meansfor individualizing saidgalvanometers to said bridges to permit the successive balancing of saidbridges.

4. A compound Wheatstone bridge for designing relay windings comprisingone bridge com-. posed of variable resistances calibrated to representthe number of turns, total resistance, the reciprocal of the resistivityfactor and the diameter of the core plus the depth of the coil and asecond bridge composed of variable resistances calibrated to representthe depth of the coil, the effective cross-section of a turn of wire,the numaesrooe' 1,3 ber of turns and the length of the coil, means forsimultaneously adjusting the value of the two resistances representingthe number of turns, of

the two resistances .representing the depth of the coil and of the tworesistances representing the reciprocal of the resistivityand theefiective crosssection, means for individually adjusting the remainingresistances and a galvanometer for each bridge to indicate when a.balance has been reached.

5. A compound Wheatstone bridge for designing relay windings comprisingone bridge composed of variable resistances calibrated to represent thenumberof turns, the total resistance, the reciprocal of the resistivityfactor and the diameter of the core plus the depth of the coil and asecond bridge composed of variable resistances calibrated to representthe depth of the coil, the efiective cross-section of aturn of wire, thenumberof turnsand the length of the coil, means for simultaneouslyadjusting the values of the two resistances representing the number ofturns, of the two resistances representing the depth of the coil and ofthe two resistances representing the reciprocal .of the resistivity andthe effective cross-section, means for individually adjusting theremaining resistances, a galvanometer for each bridge to indicate when abalance has been reached, and means for adapting said second bridge toexpress relaydesign in terms of layers of wire comprising a variableresistance calibrated to represent the number of layers, a variableresistance calibrated to represent the depth of one layer, a fixedresistance and switching means for simultaneously Substituting saidlastthree resistances for the resistances representing the m r of ur s t e.ClQSs-section of one wire and the length of the core respectively.

6. A compound Wheatstone bridge for designing relay windings comprisingone bridge composed of variable resistances calibrated to represent thenumber of turns, the total resistance,

the reoiprocal of the resistivity factor and the diameter of the coreplus the depth of the coil and a second bridge composed of variableresistances calibrated to represent the depth of the coil, the efiectivecross-section of a turn of wire, the number of turns and the length ofthe coil, means for simultaneuosly adjusting the values of the tworesistances representing the number of turns, of the two resistancesrepresenting the depth of the coil and of the two resistancesrepresenting the reciprocal of the resistivity and the effectivecross-section, means for individually adjusting the remainingresistances, a galvanometer for each bridge to indicate when a balancehas been reached, and means for adapting said second bridge to expressrelay design in terms of layers of wire comprising a variable resistancecalibrated to represent the number of layers, a variable resistancecalibrated to represent the depth of one layer, a fixed resistance andswitching means for simultaneously substituting said last threeresistances for the resistances representing the number of turns, thecross-section of one wire and the length of the core respectively, saidresistance representing the number of layers being adjustableindependently of said first bridge,

7. A compound Wheatstone bridge for designing relay windings comprisingone bridge composed of variable resistances calibrated to represent thenumber of turns, the total resistance, the reciprocal of the resistivityfactor and the diameter of the core plus the depth of the coil and a 14second bridge composed of variable resistances calibrated torepresentthe depth of the coil, the effective cross-section of a turn of wire,the number of turns and the length of the coil, means for simultaneouslyadjusting the values of the two resistances representing the number ofturns, of the two resistances representing the depth of the coil and ofthe two resistances representing the reciprocal of the resistivity andthe effective cross-section, means for individually adjusting theremaining resistances, a galvanometer for each bridge to indicate when abalance has been reached, and means for adapting said second bridge toexpress relay design in terms of turns per layer, comprising a variableresistance calibrated .to represent the number of turns in one layer, avariable resistance calibrated to repre,

sent the depth of one layer and switching means.

for simultaneously substituting said last two resistances ,for theresistance representing the number ofturns and the resistancerepresenting the crossesection of .one wire respectively.

8. A compound Wheatstone bridge for designing relay windings comprisingone bridge composed of variable resistances calibrated to represent the,number of turns, the total resistance, the reciprocal of theresistivity factor and the diameter ,of the core plus the depth of .thecoil and a second bridge composed of variable resistances calibrated torepresent the depth of the coil, the effective cross-section ofa turnofwire, the number of turns and the length of the coil, means forsimultaneously adjusting'the values of the two resistances representingthe number of turns, of the two resistances representing .the depth ofthe coil and of the two resistances representingthe reciprocal of theresistivity and the effective cross-section, means for individuallyadjusting the remaining resistances, a galvanometer for each bridge toindicate when a balance has been reached, and means for adapting saidsecondbridge to express relay design in terms of turns per layer,comprising a variable resistance calibrated to represent the number ofturns in one layer, a variable resistance calibrated to represent thedepth of one layer and switching means for simultaneously substitutingsaid last two resistances for the resistance representing the number ofturns and the resistance representing the cross-section of one wirerespectively, said resistance representing the number of turns in onelayer being adjustable independently of said first bridge.

9. A compound Wheatstone bridge for designing relay windings comprisingone bridge having as arms variable resistances calibrated to representthe number of turns, the total resistance, the reciprocal of theresistivity factor and th diameter of the core plus the depth of thecoil and a second bridge having as arms variable resistances calibratedto represent the depth of the coil, the average effective cross-sectionof a turn of wire, the number of turns and the length of the coil, meansfor simultaneously adjusting the values of the two resistancesrepresenting the number of turns, of the two resistances representingthe depth of the coil and of the two resistances representing thereciprocal of the resistivity and the average efiective cross-section,means for individually adjusting the remaining resistances, agalvanometer for each bridge to indicate when a balance has beenreached, a resistance representing the maximum efiective cross-sectionof a wire and a resistance representing the depth of one layer of turns,the means for adjusting the resistances representing the averageefiective' cross-section ofa wire being efiective to adjust said lasttwo resistances, switching means for substituting either one of saidlast two resistances for said resistance representing the averageeffective cross-section, means for correspondingly adjusting an adjacentarm of said bridge, said bridge when balanced indicating the relaydesign in terms of the substituted quantities.

10. A compound Wheatstone bridge for designing relay windings comprisingone bridge having as arms variable resistances calibrated to representth number of turns, the total resistance, the reciprocal of theresistivity factor and the diameter of the core plus the depth of thecoil and a second bridge having as arms variable resistances calibratedto represent the depth of the coil, the efiective cross-section of aturn of wire, the number of turns and the length of the coil, means forsimultaneously adjusting the values of the two resistances representingthe number of turns, of the two resistances representing the depth ofthe coil and of the two resistances representing the reciprocal of theresistivity and the efiective cross-section, means for individuallyadjusting the remaining resistances, a galvanometer for each bridge toindicate when a balance has'been reached, said resistance representingthe effective cross-section of a turn of wire comprising a plurality ofindividual variable resist ances each corresponding to a different typeof insulation and means for rendering one of said individual resistancesefiective.

11. A compound Wheatstone bridge for designing relay windings comprisingone bridge having as arms variable resistances calibrated to representthe number of turns, the total resistance, th reciprocal of theresistivity factor and the diameter of the core plus the depth of thecoil and a second bridge having as arms variable resistances calibratedto represent th depth of the coil, the

average effective cross-section of a turn of wire,-

the number of turns and the length of the coil, means for simultaneouslyadjusting the values of the two resistances representing the number of16 turns, of the two resistances representing the depth of the coil andof the two resistances representing the reciprocal of the resistivityand the efiective cross-section, means for individually adjusting theremaining resistances and a galvan'ometer for each bridge to indicatewhen a balance has been reached, resistances representing the maximumeifective cross-section of a wire and resistances representing the depthof one layer of turns, the means for adjusting the resistancerepresenting the average effective crosssection of a wire beingeffective to also adjust said last two resistances, switching means forsubstituting either one of said last two resistances for said resistancerepresenting the average effective cross-section and correspondinglyadjusting an adjacent arm of the bridge, said resistances representingthe average eifective cross-section of wire, the maximum effectivecross-section of wire, the depth of one layer and the reciprocal of theresistivity factor, each comprising a plurality of individual variableresistances arranged in sets corresponding to different types ofinsulation and means for rendering any one of said sets of individualresistances efiective, said bridge when balanced indicating the relaydesign in terms of the substituted quantities.

WILLIAM KEISTER.

REFERENCES CITED The following references are of record in the file ofthis patent:

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